Course Syllabus

Course Description:

This course reviews and extends the concepts of elementary algebra, with problem solving skills emphasized throughout. Topics that are reviewed and extended include linear and quadratic equations, factoring polynomials, rational expressions, exponents, radicals, equations of lines, and systems of equations. New topics include graphs and their translations and reflections, functions, exponential and logarithmic functions, graphs of quadratic functions, conic sections, nonlinear systems of equations, polynomial, rational, and absolute value inequalities, sequences, series, and the Binomial Theorem.

Student Learning Outcomes:

Upon successful completion of the course, students will be able to:

• simplify expressions and solve equations involving absolute values, polynomials, rational expressions, radicals, exponentials, and logarithms.
• solve systems of equations and solve linear, polynomial, rational, and absolute value inequalities.
• demonstrate an understanding of the definition of a function and use function notation, including the algebra of functions, composite functions, and inverse functions.
• sketch the graphs of basic functions, quadratic functions, transformations of these functions, and conic sections.
• apply algebraic methods when solving word problems.

Course Content:

• Linear Equations and Inequalities: solving equations, applications, inequalities, and absolute value equations and inequalities
• Quadratic Equations and Inequalities: factoring, completing the square, the quadratic formula, applications, quadratic inequalities, graphing quadratic functions
• Graphs and Functions: definition and function notation, intercepts, domain and range, graphs of basic functions including x^3, 1/x, square root, cube root, and absolute value, transformations of functions including horizontal and vertical shifting, vertical scale factor and reflections, functions as mathematical models, algebra of functions, composite functions, inverse functions
• Linear Functions: slope, equations of lines including slope-intercept form and point-slope form, applications
• Polynomial Functions: factoring higher degree polynomials including sum and difference of cubes and expressions with quadratic form, solving polynomial equations, applications, long division of polynomials, synthetic division, the Remainder Theorem, finding a polynomial given its real zeros, polynomial inequalities
• Rational Expressions, Equations, and Functions: integer exponents, factoring expressions containing integer exponents, rational expressions and functions, adding, subtracting, multiplying and dividing rational expressions, solving rational equations, variation, applications, rational inequalities
• Radicals and Complex Numbers: radicals and rational exponents, factoring expressions containing rational exponents, simplifying radical expressions, adding, subtracting, multiplying and dividing radical expressions, rationalizing binomial denominators, solving radical equations, operations on complex numbers and applications
• Conic Sections: midpoint formula, distance formula, graphs of parabolas (vertical and horizontal), circles, ellipses, hyperbolas, translations of each conic, identify conic sections from their equations, complete the square to write the equation in standard form
• Exponential Functions: graphs and transformations; solve exponential equations; modeling exponential growth and decay; the natural base
• Logarithmic Functions: definition and notation; common logs, natural logs and change-of-base; properties of logarithms; solve logarithmic equations; logarithmic functions and their graphs; applications
• Systems of Equations and Inequalities: substitution and addition methods of solving 2 by 2 and 3 by 3 linear systems of equations, non-linear systems of equations, systems of inequalities, and applications
• Systems of Equations and Inequalities: substitution and addition methods of solving 2 by 2 and 3 by 3 linear systems of equations, non-linear systems of equations, systems of inequalities, and applications

Textbook:

Great news: your textbook for this class is available for free online!
Intermediate Algebra from OpenStax, ISBN 1-947172-03-4 

You have several options to obtain this book:

• View online (Links to an external site.) (Links to an external site.)
• Download a PDF (Links to an external site.) (Links to an external site.)
• Order a print copy (Links to an external site.) (Links to an external site.) 

You can use whichever formats you want. Web view is recommended -- the responsive design works seamlessly on any device.

Important Notes:

• All first week assignments need to be completed and submitted by the due date to avoid possibly being dropped from the class.